I had the same problem when I set up my cage. The cage "bottom" is actually just a plastic sheet that slides into the cage. It didn't support the cage and definitely didn't protect from leaking.
I ended up buying the LLLReptile "Screen Cage Water Tray" for the size of my tray. Worth the money, IMO. The screen cage sits inside the tray, so it catches water. So of course, then I had a flooding problem. "If You Give a Mouse a Cookie" syndrome
I then cored a hole in one corner and siliconed in simple sink drain assembly from a hardware store. Attached some vinyl tubing to the drain assembly, directed it to a bucket and POOF, easy cage drain. Shimmed it up on two sides to facilitate drainage, and it works like a charm. I'm a little handy, not super handy, but I was able to do this myself without much trouble.
The only catch is because the drain is in the bottom, you have to have a setup that allows the drain assembly and hose to extend down. I did this by using an end table smaller than my cage size...which would not have worked without the cage tray anyway.
The standard bottom is designed to sit inside the cage tray also, and that will help prevent feeders from escaping.
Cage Bottom Tray:
http://lllreptile.com/store/catalog...-cages/-/24-x-24-x-48-screen-cage-water-tray/
Drain Assembly (without overflow):
http://www.homedepot.com/p/t/100573...toreId=10051&N=5yc1v&R=100573448#.UWCiBFeqY4I
Vinyl Tube (purchase by the foot at HD, make sure inner diameter fits around your drain assembly, use a hose clamp to hold it in place):
http://www.homedepot.com/p/t/100162...toreId=10051&N=5yc1v&R=100162815#.UWCikVeqY4I
Quick-Cure Silicone Caulk:
http://www.homedepot.com/p/t/100004...toreId=10051&N=5yc1v&R=100004845#.UWCjg1eqY4I
There are also TONS of people who have far more elegant assemblies that what I did. There is a permanent post under the Enclosures forum dealing with cages and drains. You should look through what others have shared and marvel